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<ol>
<li>通带增益恒定为1</li>
<li>阻带增益恒定为0</li>
<li>过渡带为0</li>
</ol>
<h1 id="理想滤波器为什么不可实现"><a href="#理想滤波器为什么不可实现" class="headerlink" title="理想滤波器为什么不可实现"></a>理想滤波器为什么不可实现</h1><p>那么为什么理想滤波器是不可实现的，只能去逼近呢？查阅课本和网络告诉我们，理想滤波器的h(t)在t<0时不为0，**不满足因果性**  。<sup id="fnref:1"><a href="#fn:1" rel="footnote"><span class="hint--top hint--error hint--medium hint--rounded hint--bounce" aria-label="不过因果律是恒成立的真理吗？现在看来，是的，即使是相对论也不违反因果律（量子论俺实在没弄懂）。也许随着科学的发展，某一天因果律也会被证伪呢？
">[1]</span></a>&lt;/sup&gt;我还没有看到证明<sup id="fnref:2"><a href="#fn:2" rel="footnote"><span class="hint--top hint--error hint--medium hint--rounded hint--bounce" aria-label="挖个坑，以后把证明补上
">[2]</span></a></sup>，那么只能先感性的角度去理解这个关系。</p>
<p>首先，理想滤波器很明显满足一个特点，便是存在间断点。间断，从时域来看，例如冲激函数、单位阶跃函数，代表着在信号值瞬间迅速变化，对应着高频分量不为0。考虑极限的思想，在时域是瞬间变化，那么在频域应当是频率趋于无穷<sup id="fnref:3"><a href="#fn:3" rel="footnote"><span class="hint--top hint--error hint--medium hint--rounded hint--bounce" aria-label="那为什么正负无穷都有呢？这是因为信号是实信号，频域满足共轭偶对称。
">[3]</span></a></sup>。以此类推，频域存在间断点，那么也代表着时域存在无穷的信号<sup id="fnref:4"><a href="#fn:4" rel="footnote"><span class="hint--top hint--error hint--medium hint--rounded hint--bounce" aria-label="这里目前不知道怎么说明时域正负信号都有">[4]</span></a></sup>。</p>
<p>其次看到网上的一个观点，时域的有限对应频域的无限，反之亦然。从直观上来感觉，这个是对的，这个观点便应该触及该问题的本质了。</p>
<p>（Y.D.X指出，可以从不确定性原理入手。不确定性原理描述不同表象间的关系，正是使用了Fourier变换，这个思路很有可能是正确的。待日后有时间补上详细证明）</p>
<div id="footnotes"><hr><div id="footnotelist"><ol style="list-style: none; padding-left: 0; margin-left: 40px"><li id="fn:1"><span style="display: inline-block; vertical-align: top; padding-right: 10px; margin-left: -40px">1.</span><span style="display: inline-block; vertical-align: top; margin-left: 10px;">不过因果律是恒成立的真理吗？现在看来，是的，即使是相对论也不违反因果律（量子论俺实在没弄懂）。也许随着科学的发展，某一天因果律也会被证伪呢？<a href="#fnref:1" rev="footnote"> ↩</a></span></li><li id="fn:2"><span style="display: inline-block; vertical-align: top; padding-right: 10px; margin-left: -40px">2.</span><span style="display: inline-block; vertical-align: top; margin-left: 10px;">挖个坑，以后把证明补上<a href="#fnref:2" rev="footnote"> ↩</a></span></li><li id="fn:3"><span style="display: inline-block; vertical-align: top; padding-right: 10px; margin-left: -40px">3.</span><span style="display: inline-block; vertical-align: top; margin-left: 10px;">那为什么正负无穷都有呢？这是因为信号是实信号，频域满足共轭偶对称。<a href="#fnref:3" rev="footnote"> ↩</a></span></li><li id="fn:4"><span style="display: inline-block; vertical-align: top; padding-right: 10px; margin-left: -40px">4.</span><span style="display: inline-block; vertical-align: top; margin-left: 10px;">这里目前不知道怎么说明时域正负信号都有<a href="#fnref:4" rev="footnote"> ↩</a></span></li></ol></div></div></article><div class="tag_share"><div class="post-meta__tag-list"><a class="post-meta__tags" href="/tags/%E6%BB%A4%E6%B3%A2%E5%99%A8/">滤波器</a></div><div class="post_share"><div class="social-share" data-image="/linear-gradient(20deg,#334d50,#cbcaa5)" data-sites="facebook,twitter,wechat,weibo,qq"></div><link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/butterfly-extsrc/sharejs/dist/css/share.min.css" media="print" onload="this.media='all'"><script src="https://cdn.jsdelivr.net/npm/butterfly-extsrc/sharejs/dist/js/social-share.min.js" defer></script></div></div><div class="post-reward"><div class="reward-button"><i class="fas fa-qrcode"></i> Donate</div><div class="reward-main"><ul class="reward-all"><li class="reward-item"><a href="/img/Wechat.jpg" target="_blank"><img class="post-qr-code-img" src="/img/Wechat.jpg" alt="wechat"/></a><div class="post-qr-code-desc">wechat</div></li></ul></div></div><div class="relatedPosts"><div class="headline"><i class="fas fa-thumbs-up fa-fw"></i><span>Related Articles</span></div><div class="relatedPosts-list"><div><a href="/2022/10/%E4%BF%A1%E5%8F%B7%E5%A4%84%E7%90%86/%E5%B7%B4%E7%89%B9%E6%B2%83%E6%96%AF%E6%BB%A4%E6%B3%A2%E5%99%A8/" title="巴特沃斯滤波器"><img class="cover" src="/linear-gradient(20deg,#334d50,#cbcaa5)" alt="cover"><div class="content is-center"><div class="date"><i class="far fa-calendar-alt fa-fw"></i> 2022-10-21</div><div class="title">巴特沃斯滤波器</div></div></a></div></div></div><hr/><div id="post-comment"><div class="comment-head"><div class="comment-headline"><i class="fas fa-comments fa-fw"></i><span> Comment</span></div></div><div class="comment-wrap"><div><div id="lv-container" data-id="city" data-uid="MTAyMC81NzU3OS8zNDA0Mw=="></div></div></div></div></div><div class="aside-content" id="aside-content"><div class="sticky_layout"><div class="card-widget" id="card-toc"><div class="item-headline"><i class="fas fa-stream"></i><span>Catalog</span><span class="toc-percentage"></span></div><div class="toc-content"><ol class="toc"><li class="toc-item toc-level-1"><a class="toc-link" href="#%E4%BB%80%E4%B9%88%E6%98%AF%E7%90%86%E6%83%B3%E6%BB%A4%E6%B3%A2%E5%99%A8"><span class="toc-number">1.</span> <span class="toc-text">什么是理想滤波器</span></a></li><li class="toc-item toc-level-1"><a class="toc-link" href="#%E7%90%86%E6%83%B3%E6%BB%A4%E6%B3%A2%E5%99%A8%E4%B8%BA%E4%BB%80%E4%B9%88%E4%B8%8D%E5%8F%AF%E5%AE%9E%E7%8E%B0"><span class="toc-number">2.</span> <span class="toc-text">理想滤波器为什么不可实现</span></a></li></ol></div></div></div></div></main><footer id="footer"><div id="footer-wrap"><div class="copyright">&copy;2022 - 2023 By 杜书丞</div><div class="framework-info"><span>Framework </span><a target="_blank" rel="noopener" href="https://hexo.io">Hexo</a><span class="footer-separator">|</span><span>Theme </span><a target="_blank" rel="noopener" href="https://github.com/jerryc127/hexo-theme-butterfly">Butterfly</a></div></div></footer></div><div id="rightside"><div id="rightside-config-hide"><button id="readmode" type="button" title="Read Mode"><i class="fas fa-book-open"></i></button><button id="darkmode" type="button" title="Toggle Between Light And Dark Mode"><i class="fas fa-adjust"></i></button><button id="hide-aside-btn" type="button" title="Toggle between single-column and double-column"><i class="fas fa-arrows-alt-h"></i></button></div><div id="rightside-config-show"><button id="rightside_config" type="button" title="Setting"><i class="fas fa-cog fa-spin"></i></button><button class="close" id="mobile-toc-button" type="button" title="Table Of Contents"><i class="fas fa-list-ul"></i></button><a id="to_comment" href="#post-comment" title="Scroll To Comments"><i class="fas fa-comments"></i></a><button id="go-up" type="button" title="Back To Top"><i class="fas fa-arrow-up"></i></button></div></div><div><script src="/js/utils.js"></script><script src="/js/main.js"></script><script src="https://cdn.jsdelivr.net/npm/@fancyapps/ui/dist/fancybox.umd.min.js"></script><div class="js-pjax"><script>(() => {
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